Predicting chaos in the Newtonian three-body problem

Although chaotic dynamics limits our ability to predict individual trajectories, it may still be possible to make accurate statistical predictions. The Newtonian three-body problem offers a fascinating setting in which to explore this distinction, combining a rich history, fundamental questions in dynamical systems, and considerable astrophysical importance. In this colloquium, I will present a novel statistical theory that expresses predictions in terms of phase-space flux. Validated against extensive numerical simulations, this flux-based theory provides the most accurate statistical predictions to date for the three-body problem. I will also describe a novel dynamical reduction, introducing dynamical variables that significantly simplify the formulation of the problem. Finally, I will show how a related flux-based theory successfully predicts statistical properties of another paradigmatic chaotic system—the double pendulum—including its mean flip rate.